Police in Birmingham today arrested a Conservative city councillor who sent a Twitter message saying that the newspaper columnist Yasmin Alibhai-Brown should be stoned to death.

Alibhai-Brown said last night she would report Gareth Compton, a councillor for the Erdington district, to police following the tweet.

Compton was arrested last night and bailed after questioning. A spokeswoman for West Midlands police said: "We can confirm a 38-year-old man from Harborne has been arrested for an offence under section 127 (1a) of the Communications Act of 2003 on suspicion of sending an offensive or indecent message. He has been bailed pending further inquiries."

The Conservative party said Compton had been suspended indefinitely over the alleged tweet.

A spokesman said: "Language of this sort is not acceptable and as a result Gareth Compton's membership of the Conservative party has been indefinitely suspended pending further investigation."

Compton said the message posted yesterday on his private Twitter account had been "a glib comment" in response to the writer's appearance on Nicky Campbell's Radio 5 Live breakfast show.

The message – now apparently deleted – said: "Can someone please stone Yasmin Alibhai-Brown to death? I shan't tell Amnesty if you don't. It would be a blessing, really."

Alibhai-Brown, who writes columns for the Independent and the London Evening Standard, said last night she regarded his comments as incitement to murder. She told the Guardian: "It's really upsetting. My teenage daughter is really upset too. It's really scared us.

"You just don't do this. I have a lot of threats on my life. It's incitement. I'm going to the police – I want them to know that a law's been broken."

She added that she regarded Compton's remarks as racially motivated because he mentioned stoning.

"If I as a Muslim woman had tweeted that it would be a blessing if Gareth Compton was stoned to death I'd be arrested immediately. I don't think the nasty Tories went away."

In a statement released in a series of tweets, Compton said: "I did not 'call' for the stoning of anybody. I made an ill-conceived attempt at humour in response to Yasmin Alibhai-Brown saying on Radio 5 Live this morning that no politician had the right to comment on human rights abuses, even the stoning of women in Iran. I apologise for any offence caused. It was wholly unintentional."

It is not the first time that a Twitter comment seemingly intended as a joke has landed the sender in trouble with the law.

Later today, Paul Chambers, a 27-year old trainee accountant from South Yorkshire, is expected to hear whether he has successfully appealed against £1,000 fine for a tweet sent when snow closed Robin Hood airport near Doncaster in January when he was due to go away. He posted: "Crap! Robin Hood airport is closed. You've got a week and a bit to get your shit together otherwise I'm blowing the airport sky high!!"